Prove: `cot^2A cos e c^2B-cot^2B cos e c^2A=cot^2A-cot^2B` .

Prove that: cot^2A-tan^2A=4\ cot2A cos e c2A

Prove: tan^2A+cot^2A=sec^2A cos e c^2A-2

Prove that : cot^(2) A - cot^(2) B = (cos^(2) A - cos^(2) B)/ (sin^(2) A sin^(2) B) = cosec^(2) A - cosec^(2)B

Prove that: cot2A + tanA= cotA - cot 2A

Prove that: (cos A+cos B)/(cos B-cos A)=cot((A+B)/2)cot((A-B)/2)

Let O be a point inside a triangle A B C such that /_O A B=/_O B C=/_O C A=omega , then show that: cotomega=cotA+cotB+cot C Cos e c^2omega=cos e c^2A+cos e c^2B+cos e c^2C

Prove: 1+(cot^2theta)/(1+cos e c\ theta)=cos e c\ theta

In a A B C , if r_1+r_3+r=r_2, then sec^2A+cos e c^2B' is equal to 1-cos^2C (2) 1+cos e c^2C (4) 2-cot^2C

Prove: cos e c^6theta=cot^6theta+3cot^2thetacos e c^2theta+1

Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(sec^(-1)2)+cot^2(cos e c^(-1)3)=11